Special equipment: A 1 1/2-quart (6-cup) souffle dish
Position an oven rack in the lower third of the oven, making sure the rack above it is high enough to allow the souffle to rise a few inches above the top of a 1 1/2-quart souffle dish; preheat the oven to 375 degrees F. Using 1 tablespoon of the butter, grease the souffle dish. Place 2 tablespoons of the Parmesan in the dish and shake the dish so that the cheese coats the bottom and sides.
In a large saucepan, melt the remaining 3 tablespoons butter over medium heat. Whisk in the flour and cook, whisking continuously, until the mixtures gets a bit foamy, about 2 minutes. Whisk in the cayenne, remove the pan from the heat, whisk in the hot milk, then return the pan to the heat and simmer, whisking all the while. Add the Gruyere and the remaining 2 tablespoons Parmesan and cook, whisking, until the cheese melts and the mixture thickens, 1 to 2 minutes.
Remove the pan from the heat and whisk in the mustard, salt and pepper. Whisk in the egg yolks 1 at a time, whisking quickly until they are completely incorporated.
In a large metal bowl, use a large whisk or an electric mixer to beat the egg whites until they start to become foamy, then add the cream of tartar and continue beating until the whites form stiff peaks with a little droop at the very tip. Transfer about one-quarter of the egg whites to the yolk mixture, stir until just blended, then dump half of the rest of the whites into the yolk mixture and use a flexible spatula to gently fold them in. Repeat with the rest of the whites, folding just until barely blended with a few streaks of white remaining.
Turn the mixture into the prepared souffle dish, smooth the top and run your thumb around the inside rim to remove any bits of Parmesan and also to allow the souffle to rise to its fullest height. Bake until the top has risen about 2 inches above the rim and barely jiggles a bit when you lightly shake the dish, 25 to 30 minutes.
Serve immediately. Use a large spoon and make sure every serving includes some of the crusty outside and top and the creamier interior.
Recipe courtesy of Katie Workman